Question: A composite function can be written as $w\bigl(u(x)\bigr)$, where $u$ and $w$ are basic functions. Is $h(x)=e^{-x^2}$ a composite function? If so, what are $u$ and $w$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $h$ is composite. $u(x)=-x^2$ and $w(x)=e^x$. (Choice B) B $h$ is composite. $u(x)=e^x$ and $w(x)=-x^2$. (Choice C) C $h$ is not a composite function.
Answer: Composite and combined functions A composite function is where we make the output from one function, in this case $u$, the input for another function, in this case $w$. We can also combine functions using arithmetic operations, but such a combination is not considered a composite function. The inner function The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function. Here, we do not have any grouping symbols. However, we have to evaluate the expression for the exponent before evaluating the power. So $u(x)=-x^2$ is the inner function. The outer function Then we raise $e$ to the power of the entire output of $u$. So $w(x)=e^x$ is the outer function. Answer $h$ is composite. $u(x)=-x^2$ and $w(x)=e^x$. Note that there are other valid ways to decompose $h$, especially into more complicated functions.